Question: State whether each of the following is a continuous variable or a discrete variable. a. the number of hearts in a hand of seven playing

State whether each of the following is a continuous variable or a discrete variable.

a. the number of hearts in a hand of seven playing cards

b. the mass of an apple randomly chosen from a supermarket bin c. the time it takes to FINISH this test

2. Determine ( 8), if the mean is 7 and the standard deviation is 2. (2 marks)

3. The percentage of data less than a value, x, is 33% where the mean is 20 and the standard deviation is 2.5. Determine the value of x. (3 marks)

4. IQ scores of people around the World are normally distributed, with a mean of

100 and a standard deviation of 15. A genius is someone with an IQ greater than or equal to 140.

What percent of the population is considered genius? (3 marks)

5. The Weights of 100 remote control cars at a competition are approximately normally distributed. The average weight is 3.2 kg, with a standard deviation of 0.4 kg. (8 marks)

a. How many remote control cars would be disqualified if it were against the rules to have a car with a weight of more than 4 kg or less than 2.4 kg?

b. A car is said to be in the 90th percentile. How much does it weigh?

6. A multiple choice test has 20 questions, each with four possible answers. If students randomly guessed on every question the average number of questions answered correctly would be 5 with a standard deviation of 1.94. If this Binomial distribution is approximated with a normal curve what percentage of students would pass this test by randomly guessing on every question? (3 marks)

7. Using the statistics provided for the average annual income per person for 100 countries from aroung the world in 2022. (10 marks)

a) Determine the mean and sample standard deviation for the data set.

b) Hungary has an average annual income of $8613, what percentile does this place Hungary in?

c) Create a relative histogram and frequence polygon for the data using

d) Hungary's average income is the 68th highest of the 100 countries listed. What percentile does this actually place them in?

e) Give reasons why the answers in parts b) and d) don't match

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